Calculating the average of all odd numbers up to 100 is a straightforward process! Let’s break it down step by step:
1. **Identify the Odd Numbers:** The odd numbers from 1 to 100 are: 1, 3, 5, 7, …, 99. This can be represented as an arithmetic sequence where:
- The first term (a) = 1
- The common difference (d) = 2
- The last term (l) = 99
2. **Calculate the Total Count of Odd Numbers:**
To find the number of terms (n) in this sequence, we can use the formula for the n-th term of an arithmetic sequence:
n = (l - a) / d + 1
Substituting the values:
n = (99 - 1) / 2 + 1 = 49 + 1 = 50
So, there are 50 odd numbers from 1 to 100.
3. **Calculate the Sum of Odd Numbers:**
The sum (S) of the first n odd numbers can be calculated using the formula:
S = n^2
For our case:
S = 50^2 = 2500
4. **Calculate the Average:**
Now, to find the average (A), divide the sum by the number of terms:
A = S / n
A = 2500 / 50 = 50
So, the average of all odd numbers up to 100 is 50.
In conclusion, you can effortlessly calculate the average of odd numbers by identifying them, counting them, calculating their sum, and finally dividing this sum by the count of these numbers. Happy calculating!